Singular perturbation approximation of bounded real and of positive real transfer matrices

In this work the problem of model reduction of bounded real and of positive real transfer matrices is considered. Singular perturbation approximation of bounded real balanced and of stochastically balanced systems are proposed and their properties are shown. In particular it is shown that the reduced order models remain bounded real and positive real respectively and bounds on the approximation error are obtained. An example, showing the suitability of the proposed method, concludes the paper.